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Optical devices with asymmetric transmission have important applications in optical systems, but optical isolators with the modal asymmetry can only be built using magneto-optical or nonlinear materials, as dictated by the Lorentz reciprocity theorem. However, optical devices with the power asymmetry can be achieved by linear materials such as metals and dielectrics. In this paper, we report a large-area, nanoimprint-defined meta-surface (stacked subwavelength gratings) with high-contrast asymmetric transmittance in the visible-to-infrared wavelength range for TM-polarized light. The physical origin of asymmetric transmission through the meta-surface is studied by analyzing the scattering matrix.
© 2016 Optical Society of America
1. Introduction
Optical devices with asymmetric transmission have important applications in optical systems. Optical isolators, one subset of asymmetric optical devices, only permit transmission in one direction. They are widely used to avoid disturbance from back reflections in laser systems. However, a strict optical isolation requires breaking Lorentz reciprocity to create an asymmetric scattering matrix [1] and can be achieved with magneto-optical or nonlinear materials [2]. Such materials are not necessary to achieve asymmetric power transmission. Even if the scattering matrix of the system is symmetric, the transmitted power will still depend on the direction of incidence [3].
The design and fabrication of meta-materials has advanced rapidly due to progress in computing power and nano-fabrication technologies [4]. A variety of metallic and dielectric meta-materials designs have been proposed to realize unidirectional optical transmission [5–18]. For those designs that were successfully fabricated, high-cost and low-yield fabrication technologies were generally used, such as electron beam lithography (EBL) [19], focus ion beam (FIB) milling [20] or direct laser writing (DLW) [21]. Those techniques produce samples with a limited size and are economically difficult to scale up for practical applications. It is a remarkable fact that most of the fabricated diode-like devices with asymmetric transmissivity were made to operate in the infrared or terahertz wavelength ranges. So far, the only asymmetric optical device operating in the visible range was reported in 2014 [14], which incorporated cascaded gratings and hyperbolic meta-materials patterned with FIB milling. However, the device area was small (10 μm × 10 μm) and its absolute transmittance was low (with an average transmittance below 5%). Since light in the visible range has a significantly shorter wavelength than in the infrared or terahertz ranges, optical devices in the visible require a smaller feature size. In addition, the selection of materials is limited by the requirement of low optical loss. Therefore, low-loss optical devices with asymmetric transmission in the visible range are challenging to accomplish and necessitate improved design strategies and fabrication techniques.
In this paper, we report the first experimental demonstration of a large-area meta-surface (stacked subwavelength gratings) with high-contrast asymmetric transmittance in the visible-to-infrared wavelength range. The meta-surface has a diode-like optical transmission for polarized light. In this work, nanoimprint lithography (NIL) [22] was used to pattern high-resolution structures over a very large area (2 cm × 2 cm). The technique offers low cost, high yield and excellent scalability of mass production for practical applications. Compared to previous results, our diode-like meta-surface device can operate over a broad band from the visible to near-infrared. Moreover, it has excellent optical transmittance and extinction ratio for visible wavelengths, compared with most previously published asymmetric diode-like optical meta-materials built with linear and isotropic materials.
2. Design and simulation
The schematic of the meta-surface is shown in Fig. 1. There are three layers on top of the SiO2 substrate: a layer of plasmonic, subwavelength aluminum (Al) metallic gratings [23], a planarization layer (made of UV curable NIL resist), and a layer of birefringent subwavelength gratings (made of SiNx) [24, 25]. Realizing asymmetric transmission through stacked dielectric and metallic gratings have been reported theoretically in IR range [5], in which dielectric gratings were designed as a half-wave plate. To make the design work in visible range and possible to fabricate, many trade-offs were made on choice of material, grating pitch and line width. In addition, a thin planarization layer was utilized for a compact implementation. As shown in Fig. 1, the metallic gratings (along the y axis) and the dielectric gratings are aligned at a 45 degree angle with respect to each other. Such a rotation angle (45 degree) can simplify the alignment in fabrication and analysis using scattering matrix. For y-polarized (i.e. TM-polarized) light, the meta-surface can demonstrate a diode-like asymmetric transmission. When the light impinges from the bottom of the device along the positive z axis (defined as the forward incidence direction), most of energy will be blocked. When the light impinges from the top along the negative z axis (defined as the backward incidence), a substantial part of energy will be transmitted. Such asymmetric power transmission does not require the breaking of Lorentz reciprocity, and it will be discussed later in this paper.
The plasmonic metallic gratings work as a wire grid polarizer [23]. Only light with polarization perpendicular to the grating direction can be transmitted. To avoid any higher-order diffraction, the period of the grating must be smaller than wavelength. The filling ratio of the gratings is not very critical, and the grating should be deep enough to ensure a good extinction ratio.
The SiNx grating on top should also be subwavelength to avoid any higher-order diffraction. The SiNx grating works as a birefringent medium, with different effective refractive indices for polarization parallel to the grating (o axis) and perpendicular to the grating (e axis). The filling ratio of the grating will determine the difference in refractive indices, ne − no. The height of the grating determines the amount of phase difference between light in the o and e axes.
Major tradeoffs were made in the SiNx gratings that should be designed as a meta-surface with high optical anisotrosopy to improve the optical transmittance. The dutycycle of the grating decides the index diffrence between o and e axes, no − ne. As plotted in Fig. 2, a grating width of 150 nm is optimal with a peak value of 0.32. In order to make a half-wave plate for 500 nm, the height of the grating should be larger than 800 nm. If the gratings are too high, grating bars will easily collapse to fail the device. Therefore, we have to limit the height of our grating to be 510 nm to avoid collapsing. Theoretically, higher gratings (with the same dutycycle) can further enhance the average transmission of the device, as shown in Fig. 3(a). Another possible way to improve the optical performance is to use materials with higher refractive index, and its affect on the average transmission can be seen in Fig. 3(b).
Fig. 3 (a) Average transmittance (450 nm – 1000 nm) under different height of grating (n = 2) (b) Average transmittance (450 nm – 1000 nm) under difference refractive indices of grating (height = 500 nm)
When y-polarized light is incident from the top, it goes through the dielectric layer first before impinging on the metallic grating. The birefringence effect will turn the y-polarized light into elliptically-polarized light (with an x-polarized component). The energy from the x-polarized light will transmit through the metallic grating, resulting in a high transmittance. On the contrary, when y-polarized light comes in from the bottom, all the energy will be blocked by the metallic grating, resulting in a low transmittance.
The medium between gratings serves as a buffer (planarization) layer to fill the gap of the metallic gratings and support the top gratings, so the thickness of that layer should be larger than the height of the metallic grating. To study how its thickness would affect the device performance, the transmittance in both forward and backward directions for different buffer layer thicknesses were computed using both finite-difference time-domain method (FDTD) [26] and rigorous coupled-wave analysis (RCWA) [27], as shown in Fig. 4.
Fig. 4 (a) Forward transmittance under different buffer layer thicknesses (i.e. the distance between top grating and substrate); (b) Backward transmittance under different buffer layer thicknesses (i.e. the distance between top grating and substrate)
Backward transmittance is close to zero under all distances between top grating and substrate, because the metallic gratings block the incident light coming from the bottom. However, forward transmittance is affected by the buffer layer thicknesses. With the increase of buffer layer thickness, the peak in transmittance spectrum shifts to longer wavelength and the separation between adjacent peaks also increases. Since the effective refractive index of the gratings and the buffer layer are not the same, reflection will occur on both ends of buffer layer. The buffer layer acts like a low-Q resonance etalon. The relationship between the average transmittance and the thickness of buffer layer is plotted in Fig. 5, from which we can see that this device doesn’t rely any near field coupling between the Al grating and SiNx grating layer. In this arrangement, the spatial asymmetry of the structure is created for the asymmetric transmission of a certain polarization.
Fig. 5 Average transmittance (450 nm to 1000 nm) under different distance (buffer layer thicknesses)
3. Device fabrication
The gratings in the meta-surface were fabricated with NIL (followed by residual layer etching, Cr lift-off process). The large-area silicon master mold in NIL was fabricated with interference lithography [28]. A hybrid mold nanoimprint process [29] was used to transfer the pattern on the master mold. The line width tuning and edge smoothening processes [30] were used for better fabrication results.
The fabrication of the meta-surface started with patterning one-dimensional (1D) Al grating (pitch: 146 nm, width: 68 nm, height: 190 nm) on a SiO2 substrate, as shown in Fig. 6(a). Then, the UV curable resist was spun (30 sec@1200 rpm) on to the 1D Aluminum grating and cured under UV light in a nitrogen environment for 10 min to form a buffer layer with a thickness of 355 nm, as shwon in Fig. 6(b). After that, SiNx (thickness: 510 nm) was deposited with plasma-enhanced chemical vapor deposition (PECVD) at a temperature of 300 °C, as shown in Fig. 6(c). Last, a 1D grating (pitch: 245 nm, width: 80 nm, height: 510 nm) was patterned on the SiNx layer using NIL and reactive ion etching, as shown in Fig. 6(d). The scanning electron microscopic (SEM) image of the fabricated meta-surfaces is shown in Fig. 7.
Fig. 6 The fabrication process of the meta-surface: (a) pattern metallic gratings on SiO2 substrate (b) spin on UV curable resist as the buffer layer; (c) PECVD SiNx; (d) pattern SiNx gratings on buffer layer
4. Device measurement
The transmittance was measured with a spectrometer (Ocean Optics HR-4000). The transmittance (x-polarized and y-polarized) of the metallic gratings and its extinction ratio are plotted in Fig. 8. In the visible-to-near-infrared range (400 nm – 850 nm), the fabricated metallic gratings have over 80 % transmittance and an extinction ratio of around 50 dB. The forward and backward transmittance of the fabricated meta-surface are plotted in Fig. 9. For forward direction, the average transmittance reaches 28 % over visible-to-near-infrared range (400 nm – 850 nm) with a peak value of 37 %(at 450 nm). For backward transmittance, the absolute value is generally less than 1 % and the diode-like performance has an extinction ratio of 30 dB over a broadband range.
Fig. 9 Transmittance (Forward and Backward) and extinction ratio of the fabricated meta-surface with asymmetric transmission
In Fig. 9, the measured and simulated transmittance are compared and a good agreement can be observed. The differences are mainly caused by the fabrication error, nanoimprint nonuniformity and scattering from surface roughnesses. The peaks in the transmittance curve are the result of multiple reflection effect in the buffer layer, which can be treated as a resonance cavity. Since the reflectivity at both ends of the cavity is low, so the effect is relatively weak and the quality factor (Q) of the resonance peak is not high. Generally, except those resonance peaks, as the wavelength becomes higher, the transmission becomes relatively lower. Since the meta-surface is composed of gratings, its optical performance will be dependent on the angle of incidence. Under normal incidence, since the gratings are subwavelength for visible light, there will be no higher order diffraction, so the device can be treated a two-port system (like a optical diode).
Compared to other asymmetric devices in recent publications, our work is quite unique. It operates in the visible-to-near-infrared range with a high absolute transmittance and extinction ratio. Moreover, thanks to nanoimprint lithography, the fabricated meta-surfaces have a large sample size, as shown in Fig. 10. The LED screen (with polarized light) in the background is the light source and mobile phone camera is the detector. By flipping the meta-surface while keeping the same metallic grating orientation, its optical property changed dramatically from completely blocking the image to partially showing the image.
Fig. 10 Real photos of (a) blocking the image on screen (b) showing the image on screen after flipping the sample
5. Discussion
The meta-surface consists of linear and isotropic materials, so its scattering matrix must be symmetric, as dictated by the Lorentz reciprocity theorem. The observed unidirectional transmission is just an asymmetry in power transmission under y-polarized incidence, while the modal transmission is still symmetric.
To simplify the theoretical analysis without any compromise of physical correctness and generality, several assumptions were made for the meta-surfaces. First, the metallic grating is assumed to be a perfect polarizer that blocks all y-polarized light and transmits x-polarized light. Second, the dielectric grating on top is assumed to be a birefringent media with different refractive indices along the o axis and e axis. Third, both components still work the same when they are put together, with negligible near-field coupling effects. Last, the reflections between adjacent layers are neglected. Based on the above assumptions, the schematic of meta-surface is shown in Fig. 11. In this system, there are two ports (along the positive and negative z axes) and each port contains four different modes: incoming x-polarized, incoming y-polarized, outgoing x-polarized, and outgoing y-polarized.
The birefringent media will partially convert x-polarized light into y-polarized light (Txy) and y-polarized light into x-polarized light (Tyx). Due to the symmetry in the structure, Txy is equal to Tyx, and Txx is the same as Tyy. Following the notations in Fig. 11, the scattering matrix of the entire meta-surface can be written as,
Noting that Txx = Tyy and Txy = Tyx, the scattering matrix is symmetric, which means that the system has a strict modal symmetry and does not violate the Lorentz reciprocal theorem. The asymmetry in power transmission can be observed when limiting the incidence to y-polarized direction.
When incidence comes in from forward direction (i.e. negative z axis), the outgoing modes can be derived using the scattering matrix,
Therefore, the transmitted power is . To increase the transmitted power, Tyx should be increased by either increasing the thickness of the dielectric grating or increasing the contrast of refractive index for o axis and e axis, as shown in Fig. 3. In our samples, they are limited by our etching capability and material availability.
For backward transmission,
The transmitted power is . Actually, the backward transmittance largely depends on the ability of the metallic grating to reject y-polarized light.
The above scattering matrix analysis reflects an important insight for the Lorentz reciprocity theorem. The scattering matrix can also be easily reduced to Jones matrix [31]. For an optical system made with linear and isotropic materials, it is physically impossible to achieve strict modal asymmetry, because the scattering matrix is always symmetric. However, by placing a limitation on the incident modes, it is possible to achieve energy transmission asymmetry, which is a loophole in the Lorentz reciprocity theorem.
6. Conclusion
Compared to previously published results (Table 1), this work reported the first experimental results that demonstrate the ability of a large-area meta-surface to unidirectionally block visible-to-near-infrared light with a large absolute transmittance (average 28 %) and extinction ratio (30 dB). The dramatic improvements of the performance were enabled by the new paradigm in the meta-surface design and large-area nanoimprint technology. The optical performance can be further improved if we use material with higher index to fabricate the dielectric gratings (such as TiO2). The nanoimprint process can also be further optimized to reduce the grating roughness and to improve patterning uniformity.
Table 1. Comparison with representative published results on optically asymmetric devices
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